Why Olympic Skaters Fall

Did you watch the figure skating the other night? Did you notice almost every skater on the ice falling and making really embarrassing gaffes? Did you perhaps compare this to a typical Icecapades where falls almost never happen, or at least don’t happen nearly as frequently? There is a reason for this, and unlike what some TV commentators say it has little or nothing to do with pressure and the new scoring system and quite a lot to do with statistics and strategy.

The first thing you need to do understand is that all the athletes who make it to the finals are truly excellent, world class athletes. There aren’t going to be any blowouts. This isn’t like Basketball or Ice Hockey or some other sports where one country can just completely dominate everyone else. Almost every one of the 24 women in the finals could beat the other 23 on the right day. They are all very near the limits of human performance, and they have to compete under that assumption.

In the Icecapades, a skater is only trying to please the audience. As long as what they do is pretty enough and impressive enough, it doesn’t have to be the best possible. It is more important not to screw up than it is to try for the best possible result. No way is an Icecapades performer going to take a jump they only have a one in three chance of landing. However the calculus of results is completely different for the Olympics.

In competitive skating at this level, you’re competing against 23 other people, all of whom have a one in three chance of landing that same (or equivalent) difficult jump. Odds are four of them are going to make it and eight are going to fall on their asses. But all three medals are going to the four who make it. To even have a chance at a medal, a skater has to attempt moves that might very well fail. They can’t hold back and only perform safe moves they know they can execute without disaster.

Now you can play with the numbers here. Maybe the moves have a 1 in 2 or 2 in 3 chance of succeeding. Perhaps the top half dozen skaters have a one in two chance of pulling off the difficult moves and the bottom six have only a one in four. Maybe even the top skater has a 52% chance of executing a tough jump perfectly, and the second place skater has a 49% chance. Of course you have to combine the chances of failure across several different moves. On any given day, the odds may not play out quite as expected. For instance, Thursday night a few more skaters had major stumbles and falls than I would expect. Some days, it’s a few less. But the basic rule remains the same.

I suspect an economist or game theorist could put some exact numbers on this. It might even be possible that when all 23 other skaters are taking big risks to aim for the gold, it might be a sensible strategy to pull back a little, not screw up, and hope the other 23 do. This may in fact be what happened Thursday night. (Has there been another major event where both silver and bronze went to skaters with big falls?) However, my gut feeling is that holding back is not an optimal strategy here, and the skaters and their coaches know it. The best way to win is to take a real chance of losing badly.

P.S. This also explains why it’s better to skate later in the program rather than sooner. I doubt it has so much to do with the judges holding back scores in the early rounds to leave room for later competitors (as I heard one commentator claim Thursday night) as it does letting the later skaters decide how much they have to risk to win. The earlier skater has to assume at least some of the later skaters will get high marks. The later skater knows whether the earlier skaters did well or not.

P.P.S. Of course this is completely dependent on the nature of the event. In figure skating anyone who gets less than bronze might as well not have shown up; and the difference between the three top spots is huge. It also matters that although each person skates individually, they are effectively competing against 23 others simultaneously. Not all games operate under these rules. In particular business is rarely a zero sum game, and being in the middle can be quite profitable. A solid shot at the middle is usually a better choice than a small chance at winning everything and large chance of losing everything. If figure skating were more directly competitive like curling or hockey where there’s a winner and a loser in each round, I don’t think this analysis would work either. But in figure skating and similarly judged sports like gymnastics, I think it explains a lot.

2 Responses to “Why Olympic Skaters Fall”

  1. Tim Says:

    Which country is it that completely dominates everyone else in ice hockey?

  2. Elliotte Rusty Harold Says:

    I don’t know that any one country does consistently dominate others in ice hockey from year to year, but in some years one team can be quite a lot better than the others. The difference between the winner and 3rd, 4th, 5th, 15th place, etc. is usually quite a lot more significant than it is in figure skating.

    It is true that team sports tend to favor larger countries much more so than individual sports like figure skating. A single world class skater from Belgium (for example) can easily compete on an equal footing with skaters from the U.S. or Russia. However a world class hockey player needs to find five other world class players in the same country to compete effectively. Obviously this is an advantage for larger countries.

    Of course team sports usually require more government or private financing (less so since professionals started playing in the Olympics).

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